Question

If the lengths of the diagonals of a rhombus are 30 cm and 40 cm, then the side of the rhombus is

• A. 15 cm
• B. 20 cm
• C. 25 cm
• D. 30 cm

Answer 1

The Correct Option is C

In a rhombus, the diagonals bisect each other at right angles. Therefore, the diagonals divide the rhombus into four right-angled triangles. The half-lengths of the diagonals form the two perpendicular sides of a right-angled triangle, and the side of the rhombus is the hypotenuse. Given:
One diagonal is 30 cm, so half of it is \( \frac{30}{2} = 15 \) cm.
The other diagonal is 40 cm, so half of it is \( \frac{40}{2} = 20 \) cm. Now, using the Pythagorean theorem to find the side \( s \) of the rhombus: \[ s^2 = 15^2 + 20^2 \] \[ s^2 = 225 + 400 = 625 \] \[ s = \sqrt{625} = 25 \, \text{cm} \]

The correct option is (C): \(25\ cm\)